Answer:
The average rate of change of [tex]f(x)=x^2 + 7x + 10[/tex] over the interval [tex]-20\leq x\leq -15[/tex] is -28.
Step-by-step explanation:
The average rate of change of function f(x) over the interval a ≤ x ≤ b is given by this expression:
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
It is a measure of how much the function changed per unit, on average, over that interval.
To find the average rate of change of [tex]f(x)=x^2 + 7x + 10[/tex] over the interval [tex]-20\leq x\leq -15[/tex] you must:
Evaluate x = -15 and x = -20 into the function f(x)
[tex]f(-15)=(-15)^2 + 7(-15) + 10=130\\f(-20)=(-20)^2 + 7(-20) + 10=270[/tex]
Applying the expression for the average rate of change we get
[tex]\frac{f(-15)-f(-20)}{-15+20} \\\\\frac{130-270}{-15+20} \\\\\frac{-140}{5}\\\\-28[/tex]
